We report on the search for electromagnetic counterparts to the nine gravitational-wave events with a $>$60% probability of containing a neutron star during the third (O3) LIGO-Virgo Collaboration (LVC) observing run with the All-Sky Automated Survey for SuperNovae (ASAS-SN). No optical counterparts associated with a gravitational wave event was found. However, thanks to its network of telescopes, the average area visible to at least one ASAS-SN site during the first 10 hours after the trigger contained $sim$30% of the integrated source location probability. Through a combination of normal operations and target-of-opportunity observations, ASAS-SN observations of the highest probability fields began within one hour of the trigger for four of the events. After 24 hours, ASAS-SN observed $>$60% of total probability for three events and $>$40% for all but one of the events. This is the largest area coverage to a depth of $g = 18.5$ mag from any survey with published coverage statistics for seven of the nine events. With its observing strategy, five sites around the world, and a large field of view, ASAS-SN will be one of the leading surveys to optically search for nearby neutron star mergers during LVC O4.
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